Our pushdown network, which we will refer to as “Differentiable Stack-RNN”, or DiffStk-RNN (to distinguish it from the original model “StackRNN”[1]}) and [2]}, is concretely instantiated as an RNN that learns to control an external stack data structure. The RNN itself consists of an input layer, a hidden layer with recurrent connections, and an output layer. The RNN process inputs in a sequence step by step, computing a hidden state:
\(\mathbf {z}_t = f_1(U \mathbf {x}_t + R \mathbf {z}_{t-1}) \) 
